A machine fills bottles with water. The amount of water in each bottle, W W\,W ml, is normally distributed with mean 480 ml. Given that 30% of bottles contain more than 483 ml
Find the value of k k\,k such that P(k<W<484)=0.45P(k < W < 484) = 0.45P(k<W<484)=0.45
The machine is adjusted so that the standard deviation of the amount of water in each bottle is now 5 ml. Following the adjustments the company manager now believes that the mean amount of water in each bottle is less than 480 ml. She takes a random sample of 25 bottles and finds the mean amount of water to be 478.7 ml. Test the company manager's belief at the 5% significance level. You should state your hypotheses clearly.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.